Find the limit of ln(cos(x))/(x^(-1)) as x approaches 0

 Exercise

$\lim_{x\to0}\left(\frac{ln\left(cos\:x\right)}{x^{-1}}\right)$

 

Evaluate the limit $\lim_{x\to0}\left(\frac{\ln\left(\cos\left(x\right)\right)}{x^{-1}}\right)$ by replacing all occurrences of $x$ by $0$

$\frac{\ln\left(\cos\left(0\right)\right)}{0^{-1}}$

 

$0^n=\infty$, only if $n$ is a negative number

$\frac{\ln\left(\cos\left(0\right)\right)}{\infty }$

 

The cosine of $0$ equals $1$

$\frac{\ln\left(1\right)}{\infty }$

 

Calculating the natural logarithm of $1$

$\frac{0}{\infty }$

 

Any expression divided by infinity is equal to zero

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